MAYBE

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict Trs:
  { plus(0(), x) -> x
  , plus(s(x), y) -> s(plus(p(s(x)), y))
  , p(s(0())) -> 0()
  , p(s(s(x))) -> s(p(s(x)))
  , times(0(), y) -> 0()
  , times(s(x), y) -> plus(y, times(p(s(x)), y))
  , exp(x, 0()) -> s(0())
  , exp(x, s(y)) -> times(x, exp(x, y))
  , tower(x, y) -> towerIter(x, y, s(0()))
  , towerIter(0(), y, z) -> z
  , towerIter(s(x), y, z) -> towerIter(p(s(x)), y, exp(y, z)) }
Obligation:
  runtime complexity
Answer:
  MAYBE

None of the processors succeeded.

Details of failed attempt(s):
-----------------------------
1) 'WithProblem (timeout of 60 seconds)' failed due to the
   following reason:
   
   Computation stopped due to timeout after 60.0 seconds.

2) 'Best' failed due to the following reason:
   
   None of the processors succeeded.
   
   Details of failed attempt(s):
   -----------------------------
   1) 'WithProblem (timeout of 30 seconds) (timeout of 60 seconds)'
      failed due to the following reason:
      
      Computation stopped due to timeout after 30.0 seconds.
   
   2) 'Best' failed due to the following reason:
      
      None of the processors succeeded.
      
      Details of failed attempt(s):
      -----------------------------
      1) 'bsearch-popstar (timeout of 60 seconds)' failed due to the
         following reason:
         
         The processor is inapplicable, reason:
           Processor only applicable for innermost runtime complexity analysis
      
      2) 'Polynomial Path Order (PS) (timeout of 60 seconds)' failed due
         to the following reason:
         
         The processor is inapplicable, reason:
           Processor only applicable for innermost runtime complexity analysis
      
   
   3) 'Fastest (timeout of 5 seconds) (timeout of 60 seconds)' failed
      due to the following reason:
      
      None of the processors succeeded.
      
      Details of failed attempt(s):
      -----------------------------
      1) 'Bounds with perSymbol-enrichment and initial automaton 'match''
         failed due to the following reason:
         
         match-boundness of the problem could not be verified.
      
      2) 'Bounds with minimal-enrichment and initial automaton 'match''
         failed due to the following reason:
         
         match-boundness of the problem could not be verified.
      
   

3) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed
   due to the following reason:
   
   We add the following weak dependency pairs:
   
   Strict DPs:
     { plus^#(0(), x) -> c_1(x)
     , plus^#(s(x), y) -> c_2(plus^#(p(s(x)), y))
     , p^#(s(0())) -> c_3()
     , p^#(s(s(x))) -> c_4(p^#(s(x)))
     , times^#(0(), y) -> c_5()
     , times^#(s(x), y) -> c_6(plus^#(y, times(p(s(x)), y)))
     , exp^#(x, 0()) -> c_7()
     , exp^#(x, s(y)) -> c_8(times^#(x, exp(x, y)))
     , tower^#(x, y) -> c_9(towerIter^#(x, y, s(0())))
     , towerIter^#(0(), y, z) -> c_10(z)
     , towerIter^#(s(x), y, z) ->
       c_11(towerIter^#(p(s(x)), y, exp(y, z))) }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { plus^#(0(), x) -> c_1(x)
     , plus^#(s(x), y) -> c_2(plus^#(p(s(x)), y))
     , p^#(s(0())) -> c_3()
     , p^#(s(s(x))) -> c_4(p^#(s(x)))
     , times^#(0(), y) -> c_5()
     , times^#(s(x), y) -> c_6(plus^#(y, times(p(s(x)), y)))
     , exp^#(x, 0()) -> c_7()
     , exp^#(x, s(y)) -> c_8(times^#(x, exp(x, y)))
     , tower^#(x, y) -> c_9(towerIter^#(x, y, s(0())))
     , towerIter^#(0(), y, z) -> c_10(z)
     , towerIter^#(s(x), y, z) ->
       c_11(towerIter^#(p(s(x)), y, exp(y, z))) }
   Strict Trs:
     { plus(0(), x) -> x
     , plus(s(x), y) -> s(plus(p(s(x)), y))
     , p(s(0())) -> 0()
     , p(s(s(x))) -> s(p(s(x)))
     , times(0(), y) -> 0()
     , times(s(x), y) -> plus(y, times(p(s(x)), y))
     , exp(x, 0()) -> s(0())
     , exp(x, s(y)) -> times(x, exp(x, y))
     , tower(x, y) -> towerIter(x, y, s(0()))
     , towerIter(0(), y, z) -> z
     , towerIter(s(x), y, z) -> towerIter(p(s(x)), y, exp(y, z)) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {3,5,7} by applications of
   Pre({3,5,7}) = {1,4,8,10}. Here rules are labeled as follows:
   
     DPs:
       { 1: plus^#(0(), x) -> c_1(x)
       , 2: plus^#(s(x), y) -> c_2(plus^#(p(s(x)), y))
       , 3: p^#(s(0())) -> c_3()
       , 4: p^#(s(s(x))) -> c_4(p^#(s(x)))
       , 5: times^#(0(), y) -> c_5()
       , 6: times^#(s(x), y) -> c_6(plus^#(y, times(p(s(x)), y)))
       , 7: exp^#(x, 0()) -> c_7()
       , 8: exp^#(x, s(y)) -> c_8(times^#(x, exp(x, y)))
       , 9: tower^#(x, y) -> c_9(towerIter^#(x, y, s(0())))
       , 10: towerIter^#(0(), y, z) -> c_10(z)
       , 11: towerIter^#(s(x), y, z) ->
             c_11(towerIter^#(p(s(x)), y, exp(y, z))) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { plus^#(0(), x) -> c_1(x)
     , plus^#(s(x), y) -> c_2(plus^#(p(s(x)), y))
     , p^#(s(s(x))) -> c_4(p^#(s(x)))
     , times^#(s(x), y) -> c_6(plus^#(y, times(p(s(x)), y)))
     , exp^#(x, s(y)) -> c_8(times^#(x, exp(x, y)))
     , tower^#(x, y) -> c_9(towerIter^#(x, y, s(0())))
     , towerIter^#(0(), y, z) -> c_10(z)
     , towerIter^#(s(x), y, z) ->
       c_11(towerIter^#(p(s(x)), y, exp(y, z))) }
   Strict Trs:
     { plus(0(), x) -> x
     , plus(s(x), y) -> s(plus(p(s(x)), y))
     , p(s(0())) -> 0()
     , p(s(s(x))) -> s(p(s(x)))
     , times(0(), y) -> 0()
     , times(s(x), y) -> plus(y, times(p(s(x)), y))
     , exp(x, 0()) -> s(0())
     , exp(x, s(y)) -> times(x, exp(x, y))
     , tower(x, y) -> towerIter(x, y, s(0()))
     , towerIter(0(), y, z) -> z
     , towerIter(s(x), y, z) -> towerIter(p(s(x)), y, exp(y, z)) }
   Weak DPs:
     { p^#(s(0())) -> c_3()
     , times^#(0(), y) -> c_5()
     , exp^#(x, 0()) -> c_7() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..